TSTP Solution File: GRP590-1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GRP590-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 21:04:23 EDT 2024

% Result   : Unsatisfiable 127.76s 20.68s
% Output   : Refutation 127.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (  25 unt;   5 typ;   0 def)
%            Number of atoms       :   39 (  38 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  322 (  14   ~;   7   |;   0   &; 301   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   76 (   0   ^  76   !;   0   ?;  76   :)

% Comments : 
%------------------------------------------------------------------------------
thf(multiply_type,type,
    multiply: $i > $i > $i ).

thf(inverse_type,type,
    inverse: $i > $i ).

thf(b2_type,type,
    b2: $i ).

thf(a2_type,type,
    a2: $i ).

thf(double_divide_type,type,
    double_divide: $i > $i > $i ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( inverse @ ( double_divide @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( inverse @ ( double_divide @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ A @ B )
      = ( inverse @ ( double_divide @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(1,negated_conjecture,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).

thf(4,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(5,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(6,plain,
    ( ( multiply @ ( multiply @ ( inverse @ b2 ) @ b2 ) @ a2 )
   != a2 ),
    inference(lifteq,[status(thm)],[5]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( ( multiply @ ( inverse @ ( double_divide @ B @ A ) ) @ a2 )
       != a2 )
      | ( ( multiply @ A @ B )
       != ( multiply @ ( inverse @ b2 ) @ b2 ) ) ),
    inference(paramod_ordered,[status(thm)],[10,6]) ).

thf(14,plain,
    ( ( multiply @ ( inverse @ ( double_divide @ b2 @ ( inverse @ b2 ) ) ) @ a2 )
   != a2 ),
    inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( inverse @ b2 )),bind(B,$thf( b2 ))]]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
      = C ),
    inference(lifteq,[status(thm)],[7]) ).

thf(47,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( double_divide @ ( inverse @ ( double_divide @ C @ ( inverse @ ( double_divide @ D @ ( inverse @ F ) ) ) ) ) @ E )
        = F )
      | ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
       != ( double_divide @ D @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[8,8]) ).

thf(48,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ D @ ( inverse @ ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ C @ B ) @ ( inverse @ ( double_divide @ C @ ( inverse @ D ) ) ) ) ) @ ( inverse @ A ) ) ) ) ) @ B )
      = A ),
    inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( O )),bind(D,$thf( inverse @ ( double_divide @ ( double_divide @ M @ K ) @ ( inverse @ ( double_divide @ M @ ( inverse @ O ) ) ) ) )),bind(E,$thf( K )),bind(F,$thf( F ))]]) ).

thf(57,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ D @ ( inverse @ ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ C @ B ) @ ( inverse @ ( double_divide @ C @ ( inverse @ D ) ) ) ) ) @ ( inverse @ A ) ) ) ) ) @ B )
      = A ),
    inference(simp,[status(thm)],[48]) ).

thf(550,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( double_divide @ ( inverse @ ( double_divide @ G @ ( inverse @ C ) ) ) @ E )
        = D )
      | ( ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ A @ B ) @ ( inverse @ ( double_divide @ A @ ( inverse @ C ) ) ) ) ) @ B )
       != ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ F @ E ) @ ( inverse @ ( double_divide @ F @ ( inverse @ G ) ) ) ) ) @ ( inverse @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,57]) ).

thf(551,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ A @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
      = B ),
    inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( A )),bind(B,$thf( inverse @ H )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( inverse @ H )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).

thf(634,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ A @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
      = B ),
    inference(simp,[status(thm)],[551]) ).

thf(698,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( double_divide @ ( inverse @ ( double_divide @ F @ ( inverse @ B ) ) ) @ D )
        = C )
      | ( ( double_divide @ ( inverse @ ( double_divide @ A @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
       != ( double_divide @ ( inverse @ ( double_divide @ ( double_divide @ E @ D ) @ ( inverse @ ( double_divide @ E @ ( inverse @ F ) ) ) ) ) @ ( inverse @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[634,57]) ).

thf(699,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ B @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
      = A ),
    inference(pattern_uni,[status(thm)],[698:[bind(A,$thf( double_divide @ G @ ( inverse @ I ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( inverse @ I )),bind(E,$thf( G )),bind(F,$thf( I ))]]) ).

thf(802,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ ( double_divide @ B @ ( inverse @ A ) ) ) @ ( inverse @ B ) )
      = A ),
    inference(simp,[status(thm)],[699]) ).

thf(1143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( double_divide @ ( multiply @ A @ B ) @ ( inverse @ D ) )
        = C )
      | ( ( inverse @ ( double_divide @ B @ A ) )
       != ( inverse @ ( double_divide @ D @ ( inverse @ C ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[10,802]) ).

thf(1144,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( multiply @ ( inverse @ B ) @ A ) @ ( inverse @ A ) )
      = B ),
    inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( inverse @ E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( B ))]]) ).

thf(1234,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( multiply @ ( inverse @ B ) @ A ) @ ( inverse @ A ) )
      = B ),
    inference(simp,[status(thm)],[1144]) ).

thf(1632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( double_divide @ ( inverse @ B ) @ ( inverse @ D ) )
        = C )
      | ( ( double_divide @ ( multiply @ ( inverse @ B ) @ A ) @ ( inverse @ A ) )
       != ( double_divide @ D @ ( inverse @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1234,802]) ).

thf(1633,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ B ) @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) )
      = A ),
    inference(pattern_uni,[status(thm)],[1632:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( multiply @ ( inverse @ G ) @ F ))]]) ).

thf(1735,plain,
    ! [B: $i,A: $i] :
      ( ( double_divide @ ( inverse @ B ) @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) )
      = A ),
    inference(simp,[status(thm)],[1633]) ).

thf(24117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( ( double_divide @ ( inverse @ B ) @ ( inverse @ ( multiply @ ( inverse @ B ) @ A ) ) )
       != ( double_divide @ ( inverse @ ( double_divide @ C @ ( inverse @ C ) ) ) @ ( inverse @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1735,634]) ).

thf(24118,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( inverse @ ( double_divide @ B @ ( inverse @ B ) ) ) @ A )
      = A ),
    inference(pattern_uni,[status(thm)],[24117:[bind(A,$thf( I )),bind(B,$thf( double_divide @ M @ ( inverse @ M ) )),bind(C,$thf( M )),bind(D,$thf( multiply @ ( inverse @ ( double_divide @ M @ ( inverse @ M ) ) ) @ I ))]]) ).

thf(24521,plain,
    ! [B: $i,A: $i] :
      ( ( multiply @ ( inverse @ ( double_divide @ B @ ( inverse @ B ) ) ) @ A )
      = A ),
    inference(simp,[status(thm)],[24118]) ).

thf(25857,plain,
    a2 != a2,
    inference(rewrite,[status(thm)],[14,24521]) ).

thf(25858,plain,
    $false,
    inference(simp,[status(thm)],[25857]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP590-1 : TPTP v8.2.0. Released v2.6.0.
% 0.17/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n013.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Sun May 19 04:53:09 EDT 2024
% 0.25/0.38  % CPUTime  : 
% 1.06/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.33/1.06  % [INFO] 	 Parsing done (104ms). 
% 1.33/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.28  % [INFO] 	 nitpick registered as external prover. 
% 1.76/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.92/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.92/1.35  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.92/1.35  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.92/1.36  % [INFO] 	 Type checking passed. 
% 1.92/1.36  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 127.76/20.68  % [INFO] 	 Killing All external provers ... 
% 127.76/20.68  % Time passed: 20104ms (effective reasoning time: 19610ms)
% 127.76/20.68  % Axioms used in derivation (2): multiply, single_axiom
% 127.76/20.68  % No. of inferences in proof: 32
% 127.76/20.68  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 20104 ms resp. 19610 ms w/o parsing
% 127.76/20.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 127.76/20.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------